Plotting a series of Roots

• To: mathgroup at smc.vnet.net
• Subject: [mg128689] Plotting a series of Roots
• From: William Duhe <wjduhe at loyno.edu>
• Date: Sat, 17 Nov 2012 03:49:35 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
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```Bellow is a program that solves a diff eq, then finds a particular valued root for that eq. What I want to do is be able to plot how the root changes as a function of Lambda.

m = Manipulate[Module[
{ti, tf, s1},
imgSize = 375;

ti = 0;(*initial time*)
tf = 100;(*final plot time*)

s1 = NDSolve[{x'[t] == lambda, x[0] == 0}, x, {t, ti, tf}][[1]];

t1 = FindRoot[x[t] == .1 /. s1, {t, tf}];

delta[lambda] :=
Module[{times, v, s = s1[lambda]},
times = Quiet[
Chop[FindRoot[x[t] == .1 /. s, {t, #}] & /@ {tf - 1, ti + 1}]];
v = Flatten[x[t] /. s /. times];
Subtract @@ v];
Plot[delta[lambda], {lambda, 0, .007}, Frame -> True,
Axes -> False,
FrameLabel -> {"lambda", "Change in value of root"},
ImageSize -> imgSize,
Epilog -> {Text[ToString[pt, TraditionalForm], pt, {-1.25, 1}],
Red, AbsolutePointSize[4], Point[pt]}]

Column[{Plot[Evaluate[{Tooltip[x[t] /. s1, "x[t]"]}], {t, ti, tf},
PlotRange -> Automatic, AxesLabel -> {"Time", "functions"},
ImageSize -> 350, Exclusions -> Automatic],
Row[{"x[t] = 1 when ",
t1 =
Quiet[Chop[
FindRoot[x[t] == .1 /. s1, {t, #}] & /@ {tf, ti}]]}],

"\n\n"}]], {{lambda, .001}, 0.001, 0.007,
Appearance -> "Labeled"}]

```

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